Epilepsy is one of the prominent and disturbing neurological disorder and many people across the world are victims of this problem. The sudden motor disturbances in the brain cause and trigger these seizures. Due to the hypersynchronous discharges happening on the cortical regions of the brain, the activities of the motor becomes abnormal and so seizures are triggered. The seizures caused due to epilepsy are quite heterogeneous in nature and so diagnosing it is quite challenging. Electroencephalography (EEG) is the most widely used instrument for the detection of epileptic seizures. In this work, Haar and Sym8 wavelets are employed to extract the wavelet features at level 4 from EEG signals. The extracted features like alpha, beta, theta, gamma and delta are classified through the Soft Discriminant Classifier (SDC) to obtain the epilepsy risk level from EEG signals. The final results show that when Haar wavelet is employed and classified with SDC, an average classification accuracy of 95.20% is obtained and when Sym8 wavelet is utilized and classified with SDC, an average classification accuracy of 94.68% is obtained.

1. http://www.iaeme.com/IJMET/index.asp 376 editor@iaeme.com
International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 02, February 2019, pp. 376–383, Article ID: IJMET_10_02_039
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=02
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
WAVELET TRANSFORM ANALYSIS (HAAR AND
SYM8) FOR EPILEPSY CLASSIFICATION WITH
SOFT DISCRIMINANT CLASSIFIER
Harikumar Rajaguru and Sunil Kumar Prabhakar
Department of ECE
Bannari Amman Institute of Technology, Sathyamangalam, India
ABSTRACT—
Epilepsy is one of the prominent and disturbing neurological disorder and many
people across the world are victims of this problem. The sudden motor disturbances in
the brain cause and trigger these seizures. Due to the hypersynchronous discharges
happening on the cortical regions of the brain, the activities of the motor becomes
abnormal and so seizures are triggered. The seizures caused due to epilepsy are quite
heterogeneous in nature and so diagnosing it is quite challenging.
Electroencephalography (EEG) is the most widely used instrument for the detection of
epileptic seizures. In this work, Haar and Sym8 wavelets are employed to extract the
wavelet features at level 4 from EEG signals. The extracted features like alpha, beta,
theta, gamma and delta are classified through the Soft Discriminant Classifier (SDC) to
obtain the epilepsy risk level from EEG signals. The final results show that when Haar
wavelet is employed and classified with SDC, an average classification accuracy of
95.20% is obtained and when Sym8 wavelet is utilized and classified with SDC, an
average classification accuracy of 94.68% is obtained.
Keywords—Epilepsy, EEG, SDC, Haar, Sym8
Cite this Article: Harikumar Rajaguru and Sunil Kumar Prabhakar, Wavelet Transform
Analysis (Haar and Sym8) For Epilepsy Classification with Soft Discriminant Classifier,
International Journal of Mechanical Engineering and Technology, 10(2), 2019, pp. 376–
383
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=02
1. INTRODUCTION
One of the serious and chronic brain disorders which are witnessed by incessant and recurrent
seizures is epilepsy [1]. For the continuous analysis of the cortical functions of the brain, EEG
is primarily used as it has an excellent temporal resolution [2]. Interpreting EEG data mainly for
clinical reason is a very important task. Some of the widely used techniques in EEG data
processing and epilepsy classification are explained as follows. The concept of logistic
regression and nonlinear Independent Component Analysis (ICA) was analyzed by Rajaguru
et.al for classifying epilepsy from EEG signals [3]. The interictal EEG spike detection in an

2. Wavelet Transform Analysis (Haar and Sym8) For Epilepsy Classification with Soft Discriminant
Classifier
http://www.iaeme.com/IJMET/index.asp 377 editor@iaeme.com
automated sense with the help of most commonly used Artificial Neural Network (ANN) was
done by Gabor and Seyal [4]. A very narrow approach to classification of epilepsy from EEG
signals using various techniques to mitigate dimensions with different post classifier was
analyzed by Rajaguru and Prabhakar [5]. The epileptogenic focus localization in the EEG
signals in an automated system was performed by Ramabhadran et al [6]. The Modified Sparse
Representation Classifier (SRC) and Naïve Bayesian Classifier (NBC) were utilized by
Prabhakar and Rajaguru for epilepsy classification from EEG signals [7]. A blinded clinical
trial for the real time detection of epileptiform activity from the EEG signals was done by Black
et al [8]. The aggregation operators and the fuzzy techniques for classifying epilepsy from EEG
signals was done by Harikumar and Kumar et al [9]. Wavelet families for EEG signal
classification was compared and analyzed by Gandhi et al [10]. A cluster-dependent spike
detection methodology which aims to target the interpatient and intrapatient variation in the
morphology of spikes was developed by Nonclercq et al [11]. The city block distance measures
implemented for code converters technology was done for classification of epilepsy from EEG
signals by Prabhakar and Rajaguru [12]. With the help of a database of smart templates, the
detection of inter-ictal spikes was done by Lodder et al [13]. A model-based spike detection of
epileptic EEG data was proposed by Liu et al [14]. From the compressed EEG features for
detection and classification of epilepsy, the Adaboost Classifier was analyzed by Rajaguru and
Prabhakar [15]. Based on time-series sequence merging method, the detection of interictal
epileptiform discharges was done automatically by Zhang et al [16]. Support Vector Machine
(SVM) along with the famous Gaussian Mixture Model (GMM) was analyzed thoroughly for
classifying epilepsy from EEG signals by Rajaguru and Prabhakar [17]. The Hilbert transform
along with Elman Back Propagation and Multi Layer Perceptron (MLP) for epilepsy
classification from EEG signals was done by Rajaguru and Prabhakar [18]. The application of
Singular Value Decomposition (SVD) along with Expectation Maximization (EM) Based non-
linear regression was developed by Prabhakar and Rajaguru for epilepsy classification from
EEG signals [19]. The Particle Swarm dependent Sparse Representation Classifier for Epilepsy
Classification from EEG signals was done by Prabhakar and Rajaguru [20]. In this paper, the
concept of feature extraction using wavelets as a node was extracted and then it was classified
with the help of Soft Discriminant Classifier (SDC). The organization of the paper is as follows.
The materials and methods are organized in Section 2 and the post classification with SDC is
done in section 3. The results and discussion are done in section 4. It is followed by conclusion
in section 5. The block illustration of the paper is shown in Figure 1.
Figure 1 Flow Diagram of the Methodology

3. Harikumar Rajaguru and Sunil Kumar Prabhakar
http://www.iaeme.com/IJMET/index.asp 378 editor@iaeme.com
2. MATERIALS AND METHODS
From the Department of Neurology of Sri Ramakrishna Hospital, Coimbatore, the EEG data for
20 epileptic patients is obtained in European Data Format. Pre-processing of EEG signals is
given an important priority in this work. The recordings were quite long as it was recorded for
more than 55 minutes and for the sake of computational ease and operation, it is split into
epochs. Based on the reputed 10-20 International system, the 16 channel electrodes were placed
on the scalp of the epileptic patient and the recordings were obtained. Now the extraction of
features employing wavelets as node is done.
2.1. Application of Wavelet Transform
The wavelet transform is simply an extension of the classic Fourier Transform [21]. The
Fourier transform works either in time and frequency (single scale) but wavelet transforms
work on a multi-scale basis. Enormous number of scales can be decomposed from a specific
signal and this forms the most special feature of Wavelet Transform. Each scale represents a
specific coarseness of the signal, if the multi scale features are analyzed. The decomposition of
a specific signal ][ny in a multi-resolution manner is shown as follows. The specification of the
wavelet transforms are done in terms of Low Pass Filter (LPF) p and it always aims to satisfy
the Quadrature Mirror Filter condition expressed as follows
1)()()()( 11
 
zPzPzPzP
Where for the filter p , the z-transform is indicated as )(zP . The complementary High Pass
Filter (HPF) can be respectively defined as
)()( 1
 zzPzM
A sequence of filters can be obtained with the progression of the increasing length
mentioned asi ,
)()()( 2
1 zPzPzP ii 
1,...,0),()()( 2
1  IizPzMzM i
i
i
The start condition is set as 1)(0 zP . It is then mathematically expressed in terms of time
domain as a z-scale relation as expressed below:
)(][)(
)(][)(
21
21
kpmkm
kppkp
iii
iii




Where the up sampling by a factor of n is denoted as the subscript   n and the equally
sampled discrete time is represented as k . The functions )(1, ki and )(1, ki are denoted as the
normalized wavelet and scale basis function and is mathematically represented as
)2(2)(
)2(2)(
2
1,
2
1,
Ckmk
Ckpk
i
i
i
i
i
i
i
i




Where the factor of 2
2
i
means the inner product normalization, the scalar parameter is
denoted as i and the translational parameter is denoted as C respectively. The Discrete Wavelet
Transform (DWT) can be decomposed as follows:
)()()1(
)()()1(
1,)(
1,)(
kkyc
kkyb
ii
ii





4. Wavelet Transform Analysis (Haar and Sym8) For Epilepsy Classification with Soft Discriminant
Classifier
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Where )1()(ib is the approximate coefficient and )1()(ic is the detailed coefficient at a
particular resolution i respectively.
2.2. Distribution of frequency bands
At different scales and various time instants the consideration of EEG signals as a joint
superposition of various structures are analyzed. The obtained structures at various time scales
are split and sort easily with the aid of wavelet analysis. With the help of DWT, the spectral
analysis of the EEG signals is performed. For the EEG signal analysis using the wavelet
transform, two criteria have to be satisfied. The first criteria lies in the selection of the
appropriate wavelet and the second criteria lies in choosing the primary significance of the total
number of decomposition levels and is analyzed thoroughly. Choosing the total number of
decomposition levels is done based on the dominant frequency components. Those essential
parts of the EEG signal that is well correlated with the frequency is chosen and retained in the
coefficients of the wavelets for signal classification. The number of decomposition criteria
levels is chosen to be 4 and the EEG signals were easily decomposed into fine details such as
41 DD  and with one ultimate approximation 4F . With the help of Haar and Sym8 wavelets, the
performance of the tests was done and the one which gave the highest efficiency is selected
appropriately. The distribution of the EEG signals is represented in time-frequency and
therefore the statistical features are utilized. For every subband, the standard deviations, mean,
minimum and maximum approximate coefficient values of the wavelet coefficients are used.
The feature vectors which were calculated for 41 DD  frequency bands and 4F frequency band
are utilized for classification of the EEG signals with Soft Discriminant Classifier (SDC). The
extracted features from 5 different classes using Haar and Sym8 wavelets are shown in the
Tables 1 and 2 respectively.
Table 1 Analysis of Haar Wavelet
S.No Waves and its respective Rhythms
Various Wavelet
Decomposition Levels
Total No. of
coefficients
1 Delta (  ), (1-4 Hz) 5 13
2 Theta ( ), (4-8 Hz) 4 25
3 Alpha ( ), (8-13 Hz) 3 50
4 Beta (  ), (13-30 Hz) 2 100
5 Gamma ( ), (30-50 Hz) 1 200
Table 2 Analysis of Sym8 Wavelet
S.No
Waves and its respective
Rhythms
Various Wavelet
Decomposition Level
Total No. of
coefficients
1 Delta (  ), (1-4 Hz) 5 14
2 Theta ( ), (4-8 Hz) 4 28
3 Alpha ( ), (8-13 Hz) 3 53
4 Beta (  ), (13-30 Hz) 2 111
5 Gamma ( ), (30-50 Hz) 1 207
The extracted features are then fed inside the SDC classifier and finally the epilepsy risk
level classification from EEG signals is found out.

5. Harikumar Rajaguru and Sunil Kumar Prabhakar
http://www.iaeme.com/IJMET/index.asp 380 editor@iaeme.com
3. POST CLASSIFICATION WITH SOFT DISCRIMINANT CLASSIFIER
The primary intention of SDC is to determine the class to which a specific testing sample
belongs [22]. It is performed by weighing the distance between the training sample and the test
sample. Assuming that the training set vu
kQQQQ 
 ],....,,[ 21 comes from k distinct classes.
  k
k
vuk
v
kk
k QQQQ 
 ,...,, 21 Denotes the kv samples from the th
k class where

k
i
i vv
1
. Assume
1
 s
q as the testing sample. In SDC, the k class samples are utilized effectively to indicate
the test sample and it should be achieved with the least reconstruction error. By maximizing the
transformation value of the distance which is nonlinear in nature between the test samples and
the th
k class sample, the SDC is achieved easily. The SDC is mathematically expressed as
follows:
s
q
s
dql maxarg)( 
 





 
iv
r
s
r
s
qqql
1
2
explogmaxarg)( 
Where )(, qlds
q indicates the distance in between the testing sample and the th
s class, the
identification factor of q . A penalty cost is given by the parameter 0 . Supposing q belongs
to the th
s class, then q and s
rq have similar characteristics and so
2
s
rqq  is close to zero and so
s
qd can achieve the maximum value asymptotically and it is the primary reason for maximizing
s
qd .
4. RESULTS AND DISCUSSION
If the wavelet features are effectively utilized for the primary purpose of feature extraction and
when it is classified with Softmax Discriminant Classifier, dependent on the parameters like
Sensitivity, Specificity, Performance Index, Accuracy, Quality Values and Time Delay the
average results are computed in Table 3. The formulae for the Performance Index (PI),
Sensitivity, Specificity and Accuracy are given as follows
100




 

PC
FAMCPC
PI
Where Perfect Classification is denoted by PC, Missed Classification is expressed by MC
and the False Alarm is explained by FA. The Sensitivity, Specificity and Accuracy measures
are expressed mathematically by the following
100


FAPC
PC
ySensitivit
100


MCPC
PC
ySpecificit
2
ySpecificitySensitivit
Accuracy


The Quality Value QV is mathematically defined as follows
)*6*(*)2.0( msddctdlyfa
v
PPTR
C
Q



6. Wavelet Transform Analysis (Haar and Sym8) For Epilepsy Classification with Soft Discriminant
Classifier
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Where C expresses the scaling constant, Rfa specifies the number of false alarm/set,
Tdly explains the average delay of the onset classification in seconds,Pdct mentions the
percentage of perfect classification andPmsd specifies the percentage of perfect risk level missed
The time delay is mathematically expressed as follows







100
6
100
2
MCPC
DelayTime
Table 3 Analysis of Haar and Sym8 wavelets with SDC Classifier
Parameters Haar + SDC Sym8 + SDC
PC (%) 90.41 89.37
MC (%) 7.08 4.79
FA (%) 2.49 5.83
PI (%) 88.98 87.62
Specificity (%) 92.91 95.20
Sensitivity (%)
97.5 94.16
Time Delay (sec) 2.23 2.07
Quality Values 20.53 19.82
Accuracy (%) 95.20 94.68
5. CONCLUSION
On the careful analysis of the experiment, it is observed that when Haar wavelet is employed
and classified with SDC, an average classification accuracy of 95.20%, an average quality value
of 20.53, an average time delay of 2.23 seconds along with an average Performance Index of
88.98 % are obtained. Similarly, when the Sym8 wavelet is employed and classified with SDC,
an average classification accuracy of 94.86%, an average quality value of 19.82, an average
time delay of 2.07 seconds and an average Performance Index of 87.62 % is obtained. Future
works employs the usage of different kinds of wavelets along with the usage of other post
classifiers for the epilepsy classification from EEG signals.
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